A selfdual embedding of the free lattice over countably many generators into the three-generated one (Q519945)

\(\mathrm{FL}(x,y,z)\) is the free lattice on \(x\), \(y\), \( x\), and \(F(\omega)\) the free lattice on countably many generators. \(\delta\) is the unique dual automorphism of \(\mathrm{FL}(x,y,z)\) such that \(\delta(x)=x\), \(\delta(y)=y\), and \(\delta(z)=z\). Using Whitman's lemma, the author proves that \(\mathrm{FL}(x,y,z)\) includes a sublattice \(S\) which is isomorphic to \(\mathrm{FL}(\omega)\) and is such that \(\delta(S)=S\).